Lower bounds on Q of some dipole shapes

The lower bound on the radiation Q of an arbitrary electrically small antenna shape can be determined by finding the optimal electric current density on the exterior surface of the shape, such that the Q of this current radiating in free space is minimized, and then augmenting it with a magnetic current density cancelling the fields inside the shape's surface. The Q of these coupled electric and magnetic currents radiating in free space is the lower bound on Q for the given shape. The approach is exemplified and its general applicability is substantiated by computing the lower bounds of spherically capped dipoles and comparing the results to the known bounds of a sphere and a thin cylinder.